The main advancement provided by the results in this manuscript with respect to [1]} is the absence of the unphysical restriction on the number of connected components for the boundary of the region occupied by the crystalline material, by avoiding graph-like assumptions for such boundaries assumed for the specific settings of epitaxially strained thin films in [2]}, [3]}, [4]} and material voids in [5]}. In particular, with respect to [3]} we include into the analysis the dewetting regime, i.e., the presence of other fixed materials with possibly different boundary surface tensions, even if by only treating the two dimensional case, and we establish regularity results for the crystalline morphologies and instabilities satisfied by every minimizer. Furthermore, our strategy stems from the approach used in [7]} for the Mumford-Shah functional, and hence differs from the method introduced in [3]}, which instead is based on allowing displacements to attain a limit value \(\infty \) on sets with positive measure (and on technically assigning a zero cost to the elastic-energy contribution related to those sets).
